Illinois 601 15. USC M S . received 14th M a y 1970Ahtract. Starting from bare-ion pseudopotentials, net crystal potentials are evalutiied in direct space by (a) the usual linear screening technique and (b) the Thomas-Fermi method. For the metals considered (Na and AI), the potentials are quite similar, crossing outside the cores and never differing by more than 0.02 a.u. in the case of Na nor by more than 0.2 a.u. in the case of Al. The similarity of the results based on (a) and (b) suggest the use of the pseudopotential concept in conjunction with the rather general method (b) under conditions when (a) is questionable, that is whenever the zeroth order uniform electron gas solution is a poor physical approximation to the actual system under study (specific examples being molecules, insulating solids and interfaces).Methods (a) and (bj both yield shallower wells than those most often used as input information in band structure calculations and obtained by superposing atomic data.